Representations of Hopf algebras via the Tannaka-Krein formalism

In this survey talk, we review the basics of the Tannaka-Krein reconstruction formalism in detail. Both the abelianand the monoidal setting will be considered, and emphasis is placed on the following problem: given an algebraicobject of interest (typically a Hopf algebra), how can we describe its (derived) category of representations usingmonoidal categories defined via generators and relations.